Robust sign test for the unit root hypothesis of autoregression

An $\operatorname{AR}(1)$-model is considered with autoregression observations that contain gross errors (contaminations) with unknown arbitrary distribution. The unit root hypothesis for autoregression is tested. A special sign test is proposed as an alternative to the least-square test (the latter test is not applicable in this setting). The sign test is shown to be locally qualitatively robust in terms of the equicontinuity of the power.